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Research Papers: Petroleum Engineering

Uncertainty Quantification Using Streamline Based Inversion and Distance Based Clustering

[+] Author and Article Information
Jihoon Park

Department of Energy Resources Engineering,
Seoul National University,
Seoul 151-744, Korea
e-mail: jhpark86@snu.ac.kr

Jeongwoo Jin

Department of Energy System Engineering,
Seoul National University,
Seoul 151-744, Korea
e-mail: jin8146@snu.ac.kr

Jonggeun Choe

Department of Energy Resources Engineering,
Seoul National University,
Seoul 151-744, Korea
e-mail: johnchoe@snu.ac.kr

1Present address: Department of Energy Resources Engineering, Stanford University, Stanford, CA 94305, jhpark3@stanford.edu.

2Corresponding author.

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received June 30, 2014; final manuscript received July 11, 2015; published online September 29, 2015. Editor: Hameed Metghalchi.

J. Energy Resour. Technol 138(1), 012906 (Sep 29, 2015) (6 pages) Paper No: JERT-14-1200; doi: 10.1115/1.4031446 History: Received June 30, 2014; Revised July 11, 2015

For decision making, it is crucial to have proper reservoir characterization and uncertainty assessment of reservoir performances. Since initial models constructed with limited data have high uncertainty, it is essential to integrate both static and dynamic data for reliable future predictions. Uncertainty quantification is computationally demanding because it requires a lot of iterative forward simulations and optimizations in a single history matching, and multiple realizations of reservoir models should be computed. In this paper, a methodology is proposed to rapidly quantify uncertainties by combining streamline-based inversion and distance-based clustering. A distance between each reservoir model is defined as the norm of differences of generalized travel time (GTT) vectors. Then, reservoir models are grouped according to the distances and representative models are selected from each group. Inversions are performed on the representative models instead of using all models. We use generalized travel time inversion (GTTI) for the integration of dynamic data to overcome high nonlinearity and take advantage of computational efficiency. It is verified that the proposed method gathers models with both similar dynamic responses and permeability distribution. It also assesses the uncertainty of reservoir performances reliably, while reducing the amount of calculations significantly by using the representative models.

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References

Cheng, Y. , Lee, W. J. , and McVay, D. A. , 2008, “ Quantification of Uncertainty in Reserve Estimation From Decline Curve Analysis of Production Data for Unconventional Reservoirs,” ASME J. Energy Resour. Technol., 130(4), p. 043201. [CrossRef]
Jeong, D. , Jeong, K. , Baik, H. , and Choe, J. , 2013, “ Uncertainty Analyses of Basement Fracture Reservoir Performances Using Proxy Models With High-Quality History Matching,” Energy Explor. Exploit., 31(3), pp. 395–410. [CrossRef]
Jeong, D. , Jeong, K. , Baik, H. , and Choe, J. , 2013, “ Feasibility Study and Economic Analyses for the Marginal Field Development Using Proxy Models Under Uncertainty of Reservoir Characterization,” Energy Explor. Exploit., 31(6), pp. 833–846. [CrossRef]
Gu, Y. , and Oliver, D. S. , 2005, “ The Ensemble Kalman Filter for Continuous Updating of Reservoir Simulation Models,” ASME J. Energy Resour. Technol., 128(1), pp. 79–87. [CrossRef]
Arroyo-Negrete, E. , Devegowda, D. , Datta-Gupta, A. , and Choe, J. , 2008, “ Streamline Assisted Ensemble Kalman Filter for Rapid and Continuous Reservoir Model Updating,” SPE Reservoir Eval. Eng., 11(6), pp. 1046–1060. [CrossRef]
Jung, S. , and Choe, J. , 2010, “ Stochastic Estimation of Oil Production by History Matching With Ensemble Kalman Filter,” Energy Sources, Part A, 32(10), pp. 952–961. [CrossRef]
Jung, S. , and Choe, J. , 2012, “ Reservoir Characterization Using a Streamline-Assisted Ensemble Kalman Filter With Covariance Localization,” Energy Explor. Exploit., 30(4), pp. 645–660. [CrossRef]
Panwar, W. , Trivedi, J. J. , and Nejadi, S. , 2015, “ Importance of Distributed Temperature Sensor Data for Steam Assisted Gravity Drainage Reservoir Characterization and History Matching Within Ensemble Kalman Filter Framework,” ASME J. Energy Resour. Technol., 137(4), p. 042902. [CrossRef]
Wu, Z. , and Datta-Gupta, A. , 2001, “ Rapid History Matching Using a Generalized Travel Time Inversion Method,” SPE Reservoir Simulation Symposium, Houston, TX, Feb. 11–14, Paper No. SPE 66352.
He, Z. , Yoon, S. , and Datta-Gupta, A. , 2002, “ Streamline-Based Production Data Integration With Gravity and Changing Field Conditions,” SPE J., 7(4), pp. 423–436. [CrossRef]
Bhark, E. , Rey, A. , Datta-Gupta, A. , and Jafarpour, B. , 2012, “ A Multiscale Workflow for History Matching Structured and Unstructured Grid Geometries,” SPE J., 17(3), pp. 828–848. [CrossRef]
Cheng, H. , Wen, X. , Milliken, W. , and Datta-Gupta, A. , 2004, “ Field Experiences With Assisted and Automatic History Matching Using Streamline Models,” SPE Annual Technical Conference and Exhibition, Houston, TX, Sept. 26–29, Paper No. SPE 89857.
Mamghaderi, A. , Bastami, A. , and Pourafshary, P. , 2012, “ Optimization of Waterflooding in a Layered Reservoir Using a Combination of Capacitance-Resistive Model and Genetic Algorithm Method,” ASME J. Energy Resour. Technol., 135(1), p. 013102. [CrossRef]
Shi, J. , and Leung, J. Y. , 2014, “ Semi-Analytical Proxy for Vapex Process Modeling in Heterogeneous Reservoirs,” ASME J. Energy Resour. Technol., 136(3), p. 032904. [CrossRef]
Cheng, H. , Kharghoria, A. , He, Z. , and Datta-Gupta, A. , 2005, “ Fast History Matching of Finite-Difference Models Using Streamline-Derived Sensitivities,” SPE Reservoir Eval. Eng., 8(5), pp. 426–436. [CrossRef]
Kitanidis, P. K. , 1995, “ Quasilinear Geostatistical Theory for Inversing,” Water Resour. Res., 31(10), pp. 2411–2419. [CrossRef]
Lee, K. , Jeong, H. , Jung, S. , and Choe, J. , 2013, “ Characterization of Channelized Reservoir Using Ensemble Kalman Filter With Cluster Covariance,” Energy Explor. Exploit., 31(1), pp. 17–29. [CrossRef]
Lee, K. , Jeong, H. , Jung, S. , and Choe, J. , 2013, “ Improvement of Ensemble Smoother With Clustered Covariance for Channelized Reservoirs,” Energy Explor. Exploit., 31(5), pp. 713–726. [CrossRef]
Lee, H. , Jin, J. , Shin, H. , and Choe, J. , 2015, “ Efficient Prediction of SAGD Productions Using Static Factor Clustering,” ASME J. Energy Resour. Technol., 137(3), p. 032907. [CrossRef]
Schedit, C. , and Caers, J. , 2009, “ Uncertainty Quantification in Reservoir Performance Using Distances and Kernel Methods—Application to a West Africa Deepwater Turbidite Reservoir,” SPE J., 14(4), pp. 680–692. [CrossRef]
Shirman, E. , Wojtanowicz, A. K. , and Kurban, H. , 2014, “ Enhancing Oil Recovery With Bottom Water Drainage Completion,” ASME J. Energy Resour. Technol., 136(4), p. 042906. [CrossRef]
Choe, J. , 2007, Geostatistics, Sigma Press, Seoul, Korea.

Figures

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Fig. 1

Proposed method in this research: (a) procedures and (b) GTT as the difference

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Fig. 5

Log permeability of initial and inversed representative models: (a) model 1, (b) model 3, (c) model 6, (d) model 8, and (e) model 10

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Fig. 4

Travel time of models in each cluster (watercut = 0.5): (a) at well P1 and (b) at well P6

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Fig. 3

Examples of typical models from each cluster of initial reservoir models: (a) cluster 1, (b) cluster 3, (c) cluster 6, (d) cluster 8, and (e) cluster 10

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Fig. 2

Permeability distribution and streamlines of the reference field: (a) log permeability distribution and (b) generated streamlines with the well locations

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Fig. 8

Uncertainty quantification and simulation efficiency of the proposed method: (a) uncertainty quantification of the travel time at well P1 (watercut = 0.5) and (b) number of forward simulations

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Fig. 7

Comparison of watercut responses on well P6 before and after the inversion using all 100 models and 10 representative models. (a) Initial responses from 100 models, (b) history matched results from 100 models, (c) initial responses from 10 representative models, and (d) history matched results from 10 representative models.

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Fig. 6

Comparison of watercut responses on well P1 before and after the inversion using all 100 models and 10 representative models. (a) Initial responses from 100 models, (b) history matched results from 100 models, (c) initial responses from 10 representative models, and (d) history matched results from 10 representative models.

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